# How do you find the unit vector in the same direction as (-5, 3)?

Aug 13, 2017

Given a vector $\vec{v} = \left(a , b\right)$; the unit vector is:

$\hat{v} = \frac{\vec{v}}{|} \vec{v} |$

Where $| \vec{v} | = \sqrt{{a}^{2} + {b}^{2}}$

#### Explanation:

Given: $\vec{v} = \left(- 5 , 3\right)$

$\hat{v} = \frac{\text{("-5,3")}}{\sqrt{{\left(- 5\right)}^{2} + {3}^{2}}}$

$\hat{v} = \frac{\text{("-5,3")}}{\sqrt{34}}$

$\hat{v} = \left(- \frac{5}{\sqrt{34}} , \frac{3}{\sqrt{34}}\right)$